In this paper, we focus on a general linear time-invariant multi-agent system with heterogeneous actuator saturation to answer the main questions: how to achieve global consensus under the asymptotically null controllable with bounded controls [1] premise of each agent, to make breakthroughs from the perspectives of global consensus, heterogeneous actuator saturation, communication noises [2] and distributed characteristic preservation. We introduce a distributed control algorithm that incorporates a redesigned saturation function featuring a decentralized dynamic saturation level to achieve these objectives. Each component of the dynamic saturation level self-updates according to an adaptive strategy. The proposed method effectively eliminates heterogeneous actuator saturation by carefully selecting both the constant and time-varying saturation parameters in the adaptive strategy of the dynamic saturation level. Our approach achieves both state feedback and output feedback-based global consensus, with the latter utilizing a special coordinate decomposition. Numerical simulations demonstrate the efficacy of our method.